Clint wants to keep a young tree from blow- ing over during a high wind. He decides that he should tie a rope around the tree at a height of 180 cm, and then tie the rope to a stake 200 cm from the base. Allowing 30 cm of rope for doing the tying, will the 270-cm rope he has be long enough to do the job?

No, the 270 cm rope Clint has is not enough to do the job.

Explanation:

The height of tree where rope has to be tied = 180 cm

The distance of the stake from the base of the tree = 200 cm

We can say that the arrangement makes a right angle triangle, with the right angle situated at the base of the tree. The figure is attached below. Consult it for better understanding.

Length of the rope can be found by using Pythagoras theorem.

(Length of rope)² = 180² + 200²

Length of rope = 269 cm

As it is stated the additional 30cm of rope is required for tying from both ends. Total length of rope required is:

Total length of rope = 269 + 30

Total length of rope = 299 cm

As length of rope required is 299cm, the 270 cm rope Clint has is not enough to do the job.